Figure 3. Combined wit h th e fac t tha t ^ q i s a non-negativ e function , th e latte r shows that th e integra l i n formula (1.2 ) is minimal whe n al l the coordinate s of the vecto r £ are equal , an d i t i s maximal whe n on e o f the coordinate s i s equal t o 1 and th e other s ar e equa l t o zero . D Figure 4 . £^-ball s To conclude thi s sectio n le t u s give an overvie w o f known result s o n th e extremal section s o f £™-balls. • q — o o max: £ = ( ^ , ^ , 0 , . . . ,0) , Ball [Bai ] min: £ = (1,0 , ...,0), Hadwige r [Ha] , Hensle y [He] , Vaale r [V] • 0 q 2 max: £ = (1,0,... , 0), Meyer-Pajor [MeyP ] ( 1 q 2), Caetano [C] , Barthe [Bar ] ( 0 q 1) .

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2008 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.